{"id":17353,"date":"2014-10-19T14:25:32","date_gmt":"2014-10-19T18:25:32","guid":{"rendered":"https:\/\/reactivemusic.net\/?p=17353"},"modified":"2015-01-10T17:50:42","modified_gmt":"2015-01-10T22:50:42","slug":"phasor","status":"publish","type":"post","link":"https:\/\/reactivemusic.net\/?p=17353","title":{"rendered":"Phasor"},"content":{"rendered":"

Engine of time.<\/p>\n

from Wikipedia<\/cite><\/p>\n

http:\/\/en.wikipedia.org\/wiki\/Phasor<\/a><\/p>\n

\"Unfasor\"<\/a><\/p>\n

 <\/p>\n

Traveling along the outer edge of the circle, the distance goes from 0 to 2*PI radians, then starts over again. In degrees it would be 0 to 360. A clock goes from 0 to 12. In Max and Pd the phasor~ objects are normalized to run from 0.0 to 1.0. Think of flattening out the edge of the circle to a straight line.<\/p>\n

The phasor as input to a sine or cosine function generates one \u00a0cycle of a wave for each revolution – as shown in the above animation. For example, cosine would go from 0 to 1 to 0 to -1 to 0.<\/p>\n

If you graph the phasor value, it looks like a sawtooth wave – rising in a ramp from 0.0 to 1.0 then falling straight down to 0.0 to start again.<\/p>\n

With waves, the distance around the circle represents time (or phase), the projected cosine value represents amplitude.<\/p>\n

In science…<\/h5>\n

“A phasor can be considered a vector rotating about the origin in a complex plane. The cosine function is the projection of the vector onto the real axis. Its amplitude is the modulus of the vector, and its argument is the total phase\u00a0<\/span>\"\\omega. The phase constant\u00a0<\/span>\"\\theta\"represents the angle that the vector forms with the real axis at\u00a0<\/span>t<\/i>\u00a0=\u00a00.”<\/span><\/p>\n

-WIkipedia<\/cite><\/p>\n

In art…<\/h5>\n

“And the seasons they go round and round\u00a0<\/span>
And the painted ponies go up and down\u00a0<\/span>
We’re captive on the carousel of time\u00a0<\/span>
We can’t return we can only look\u00a0<\/span>
Behind from where we came\u00a0<\/span>
And go round and round and round\u00a0<\/span>
In the circle game.”<\/span><\/p>\n

-Joni Mitchell<\/cite><\/p>\n

(These lyrics happen at about 4:40 in the video…)<\/p>\n